In fact, the likelihood principle is still applicable under a rather mild independence assumption that, at least, approximately endorses some distributional characters upon observed or computed recurrent events occurring along with the time series. For instance, ([1]}; [2]}) attempted to estimate the likelihood ratio using KL divergence; ([3]}) proposed a graph-based approach and applied it in multivariate non-Euclidean data. ([4]}) developed an empirical likelihood approach to discover an unknown number of change-points via BIC. ([5]}) present a U-statistic to quantify the difference between the characteristic functions of two segments. ([6]}) generalized Mann-Whitney rank-based statistic to multivariate settings. ([7]}) improved the kernel-based method by ([8]}) with a generalized model-selection penalty.
